Fit GAMs to dispersal patterns of Ascochyta conidia

0.1 Import Data
0.2 Fit GAMs
0.3 Compare the Models
0.4 Thoughts

0.1 Import Data

See “R/wrangle_raw_data.R” for the script that handles the data import. This Rmd file focuses on the models themselves.

0.2 Fit GAMs

For reproducibility purposes, use set.seed().

set.seed(27)

0.2.1 mod1 - s(Distance)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_count_pot ~ s(dist, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.08024    0.04751   22.74   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##           edf Ref.df    F p-value    
## s(dist) 3.926  3.996 78.4  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.482   Deviance explained = 48.8%
## GCV = 0.76522  Scale est. = 0.75394   n = 334

0.2.2 mod2 - s(Distance) + Precipitation

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_count_pot ~ sum_rain + s(dist, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.816921   0.090724   9.004  < 2e-16 ***
## sum_rain    0.028779   0.008496   3.387 0.000792 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##           edf Ref.df     F p-value    
## s(dist) 3.928  3.996 80.95  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.498   Deviance explained = 50.5%
## GCV = 0.74389  Scale est. = 0.73069   n = 334

0.2.3 mod3 - s(Distance) + Windspeed

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_count_pot ~ mws + s(dist, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.64401    0.11825   5.446 1.01e-07 ***
## mws          0.12273    0.03059   4.012 7.47e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##           edf Ref.df     F p-value    
## s(dist) 3.929  3.996 81.99  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.504   Deviance explained = 51.2%
## GCV = 0.73389  Scale est. = 0.72086   n = 334

0.2.4 mod4 - s(Distance) + Windspeed + Precipitation

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_count_pot ~ sum_rain + mws + s(dist, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.473449   0.131519   3.600 0.000368 ***
## sum_rain    0.024009   0.008457   2.839 0.004808 ** 
## mws         0.108916   0.030659   3.552 0.000438 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##          edf Ref.df    F p-value    
## s(dist) 3.93  3.996 83.8  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.515   Deviance explained = 52.3%
## GCV = 0.72064  Scale est. = 0.70569   n = 334

0.2.5 mod5 - s(Distance + Windspeed) + Precipitation

## Warning in term[i] <- attr(terms(reformulate(term[i])), "term.labels"): number
## of items to replace is not a multiple of replacement length

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_count_pot ~ sum_rain + s(dist + mws, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.816921   0.090724   9.004  < 2e-16 ***
## sum_rain    0.028779   0.008496   3.387 0.000792 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##           edf Ref.df     F p-value    
## s(dist) 3.928  3.996 80.95  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.498   Deviance explained = 50.5%
## GCV = 0.74389  Scale est. = 0.73069   n = 334

0.2.6 mod6 - s(Distance) + s(Windspeed) + Precipitation

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_count_pot ~ sum_rain + s(dist, k = 5) + s(mws, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.37885    0.16680   8.267 3.59e-15 ***
## sum_rain    -0.03264    0.01760  -1.854   0.0646 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##           edf Ref.df     F  p-value    
## s(dist) 3.938  3.997 93.81  < 2e-16 ***
## s(mws)  3.928  3.996 13.56 2.09e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.566   Deviance explained = 57.8%
## GCV = 0.6497  Scale est. = 0.63051   n = 334

0.2.7 mod7 - s(Distance) + s(Windspeed)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_count_pot ~ s(dist, k = 5) + s(mws, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.08024    0.04366   24.74   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##           edf Ref.df     F  p-value    
## s(dist) 3.937  3.997 92.96  < 2e-16 ***
## s(mws)  3.917  3.995 16.04 6.03e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.562   Deviance explained = 57.3%
## GCV = 0.65392  Scale est. = 0.63659   n = 334

0.2.8 mod8 - s(Distance) + s(Windspeed) + s(Precipitation)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_count_pot ~ s(dist, k = 5) + s(mws, k = 5) + s(sum_rain, 
##     k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.08024    0.04345   24.86   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##               edf Ref.df      F p-value    
## s(dist)     3.938  3.997 93.805  <2e-16 ***
## s(mws)      1.655  1.748  1.351  0.3360    
## s(sum_rain) 3.203  3.232  3.278  0.0114 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.566   Deviance explained = 57.8%
## GCV = 0.64956  Scale est. = 0.63051   n = 334

0.2.9 mod9 - s(Distance) + s(Precipitation)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_count_pot ~ s(dist, k = 5) + s(sum_rain, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.08024    0.04393   24.59   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##               edf Ref.df     F  p-value    
## s(dist)     3.936  3.997 91.78  < 2e-16 ***
## s(sum_rain) 3.890  3.989 15.22 5.69e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.557   Deviance explained = 56.7%
## GCV = 0.66193  Scale est. = 0.64444   n = 334

0.2.10 mod10 - s(Distance) +s(Precipitation) + Windspeed

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_count_pot ~ s(dist, k = 5) + s(sum_rain, k = 5) + mws
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  -2.7406     1.4576  -1.880  0.06097 . 
## mws           1.0750     0.4099   2.623  0.00914 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##               edf Ref.df     F  p-value    
## s(dist)     3.937  3.997 93.79  < 2e-16 ***
## s(sum_rain) 3.813  3.965 11.28 8.12e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.566   Deviance explained = 57.8%
## GCV = 0.64959  Scale est. = 0.63062   n = 334

0.2.11 mod11.0 - s(Distance) + s(Windspeed) + s(Precipitation), family = tw()

This is the same as mod8 but using family = tw(), see ?family.mgcv for more on the families. The Tweedie distribution is used where the distribution has a positive mass at zero, but is continuous unlike the Poisson distribution that requires count data. The data visualisation shows clearly that the mean pot count data have this shape.

## 
## Family: Tweedie(p=1.044) 
## Link function: log 
## 
## Formula:
## mean_count_pot ~ s(dist, k = 5) + s(mws, k = 5) + s(sum_rain, 
##     k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.22821    0.04098  -5.569 5.39e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##               edf Ref.df       F p-value    
## s(dist)     3.496  3.855 123.776  <2e-16 ***
## s(mws)      1.980  2.079   0.772   0.487    
## s(sum_rain) 2.830  2.894   5.509   0.002 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.674   Deviance explained = 61.2%
## -REML = 310.11  Scale est. = 0.36397   n = 334

Try fitting the same model using a different shrinkage smoother, ts is thin- plate splines.

0.2.12 mod11.` - s(Distance, bs = “ts”) + s(Windspeed, bs = “ts”) + s(Precipitation, bs = “ts”), family = tw()

## 
## Family: Tweedie(p=1.044) 
## Link function: log 
## 
## Formula:
## mean_count_pot ~ s(dist, k = 5, bs = "ts") + s(mws, k = 5, bs = "ts") + 
##     s(sum_rain, k = 5, bs = "ts")
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.22198    0.04089  -5.429 1.11e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df       F  p-value    
## s(dist)     3.2481      4 117.660  < 2e-16 ***
## s(mws)      0.8917      4   2.005 0.000565 ***
## s(sum_rain) 2.8824      4  15.841 2.24e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.657   Deviance explained =   60%
## -REML = 319.66  Scale est. = 0.36505   n = 334

This model uses

0.2.13 mod12 - s(Distance) + s(Precipitation) + Windspeed, family = tw()

Looking at mod11.1, mws is not significant as a smoothed term, and we’d suspect it was linear anyway, so add it as a linear term only.

## 
## Family: Tweedie(p=1.044) 
## Link function: log 
## 
## Formula:
## mean_count_pot ~ s(dist, k = 5) + s(sum_rain, k = 5) + mws
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.45815    0.09542  -4.801 2.41e-06 ***
## mws          0.06588    0.02373   2.776  0.00582 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##               edf Ref.df      F  p-value    
## s(dist)     3.496  3.854 123.47  < 2e-16 ***
## s(sum_rain) 2.907  2.996  19.44 1.04e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.661   Deviance explained = 60.2%
## -REML = 312.88  Scale est. = 0.36493   n = 334

0.3 Compare the Models

0.3.1 AIC, BIC

## # A tibble: 13 x 7
##    model      df logLik   AIC   BIC deviance df.residual
##    <chr>   <dbl>  <dbl> <dbl> <dbl>    <dbl>       <dbl>
##  1 mod11.0  9.31  -320.  663.  709.     141.        325.
##  2 mod12    8.40  -332.  686.  728.     144.        326.
##  3 mod11.1  8.02  -334.  689.  730.     145.        326.
##  4 mod8     9.80  -392.  805.  847.     204.        324.
##  5 mod10    9.75  -392.  805.  846.     204.        324.
##  6 mod6     9.87  -392.  806.  847.     204.        324.
##  7 mod7     8.85  -394.  808.  845.     207.        325.
##  8 mod9     8.83  -396.  812.  849.     210.        325.
##  9 mod4     6.93  -412.  840.  871.     231.        327.
## 10 mod3     5.93  -416.  846.  873.     236.        328.
## 11 mod2     5.93  -419.  851.  877.     240.        328.
## 12 mod5     5.93  -419.  851.  877.     240.        328.
## 13 mod1     4.93  -424.  860.  883.     248.        329.

0.3.2 R²

## # A tibble: 13 x 2
##    name    value
##    <chr>   <dbl>
##  1 mod11.0 0.674
##  2 mod12   0.661
##  3 mod11.1 0.657
##  4 mod8    0.566
##  5 mod6    0.566
##  6 mod10   0.566
##  7 mod7    0.562
##  8 mod9    0.557
##  9 mod4    0.515
## 10 mod3    0.504
## 11 mod2    0.498
## 12 mod5    0.498
## 13 mod1    0.482

0.3.3 Coefficients

## 
## mod1

## (Intercept)   s(dist).1   s(dist).2   s(dist).3   s(dist).4 
##    1.080240  -13.444330    7.368783   -1.254080   -2.291845

## 
## mod2

##  (Intercept)     sum_rain    s(dist).1    s(dist).2    s(dist).3    s(dist).4 
##   0.81692128   0.02877889 -13.40978000   7.33464779  -1.25209090  -2.29384111

## 
## mod3

## (Intercept)         mws   s(dist).1   s(dist).2   s(dist).3   s(dist).4 
##   0.6440143   0.1227341 -13.4868763   7.3983152  -1.2560432  -2.2949104

## 
## mod4

##  (Intercept)     sum_rain          mws    s(dist).1    s(dist).2    s(dist).3 
##   0.47344866   0.02400933   0.10891607 -13.45271077   7.36612892  -1.25413637 
##    s(dist).4 
##  -2.29619141

## 
## mod5

##  (Intercept)     sum_rain    s(dist).1    s(dist).2    s(dist).3    s(dist).4 
##   0.81692128   0.02877889 -13.40978000   7.33464779  -1.25209090  -2.29384111

## 
## mod6

##  (Intercept)     sum_rain    s(dist).1    s(dist).2    s(dist).3    s(dist).4 
##   1.37884978  -0.03263607 -13.52238405   7.40993482  -1.25717173  -2.30322423 
##     s(mws).1     s(mws).2     s(mws).3     s(mws).4 
##   0.99626476 -10.70707340   6.66914918   0.59636619

## 
## mod7

## (Intercept)   s(dist).1   s(dist).2   s(dist).3   s(dist).4    s(mws).1 
##   1.0802395 -13.4771686   7.3732417  -1.2548767  -2.3023128   0.8682278 
##    s(mws).2    s(mws).3    s(mws).4 
##  -6.5428897   3.8305035   0.6604538

## 
## mod8

##   (Intercept)     s(dist).1     s(dist).2     s(dist).3     s(dist).4 
##     1.0802395   -13.5231892     7.4108603    -1.2572233    -2.3031202 
##      s(mws).1      s(mws).2      s(mws).3      s(mws).4 s(sum_rain).1 
##     0.3909139    -0.7059823     1.4344954     0.8082756    19.7199870 
## s(sum_rain).2 s(sum_rain).3 s(sum_rain).4 
##   328.5020104  -102.4610960     1.3525266

## 
## mod9

##   (Intercept)     s(dist).1     s(dist).2     s(dist).3     s(dist).4 
##      1.080240    -13.505613      7.398727     -1.256415     -2.301825 
## s(sum_rain).1 s(sum_rain).2 s(sum_rain).3 s(sum_rain).4 
##     -7.708430   -109.360856     34.329152     -1.330657

## 
## mod10

##   (Intercept)           mws     s(dist).1     s(dist).2     s(dist).3 
##     -2.740619      1.075017    -13.510016      7.401753     -1.256617 
##     s(dist).4 s(sum_rain).1 s(sum_rain).2 s(sum_rain).3 s(sum_rain).4 
##     -2.302155     82.075300   1298.724127   -407.240141      8.651373

## 
## mod11.0

##   (Intercept)     s(dist).1     s(dist).2     s(dist).3     s(dist).4 
##    -0.2282130    -3.7637074     1.8984225    -0.5265088    -1.1208624 
##      s(mws).1      s(mws).2      s(mws).3      s(mws).4 s(sum_rain).1 
##     0.5077483    -1.0676679     1.5218322     0.4780137    -0.9317942 
## s(sum_rain).2 s(sum_rain).3 s(sum_rain).4 
##     5.0627315    -1.2859969    -0.9520154

## 
## mod11.1

##   (Intercept)     s(dist).1     s(dist).2     s(dist).3     s(dist).4 
## -2.219778e-01 -2.921037e+00  1.309050e+00 -4.875628e-01 -1.064831e+00 
##      s(mws).1      s(mws).2      s(mws).3      s(mws).4 s(sum_rain).1 
##  6.549552e-06 -6.671605e-04  1.691059e-03  8.920753e-02 -6.612916e-01 
## s(sum_rain).2 s(sum_rain).3 s(sum_rain).4 
##  1.173167e+00 -4.027855e-01 -5.312479e-01

## 
## mod12

##   (Intercept)           mws     s(dist).1     s(dist).2     s(dist).3 
##   -0.45814928    0.06587563   -3.76782363    1.90297824   -0.52681818 
##     s(dist).4 s(sum_rain).1 s(sum_rain).2 s(sum_rain).3 s(sum_rain).4 
##   -1.12066486   -0.46302990    4.76460329   -1.55284478   -0.53564456

0.3.4 ANOVA

## Analysis of Deviance Table
## 
## Model  1: mean_count_pot ~ s(dist, k = 5)
## Model  2: mean_count_pot ~ sum_rain + s(dist, k = 5)
## Model  3: mean_count_pot ~ mws + s(dist, k = 5)
## Model  4: mean_count_pot ~ sum_rain + mws + s(dist, k = 5)
## Model  5: mean_count_pot ~ sum_rain + s(dist + mws, k = 5)
## Model  6: mean_count_pot ~ sum_rain + s(dist, k = 5) + s(mws, k = 5)
## Model  7: mean_count_pot ~ s(dist, k = 5) + s(mws, k = 5)
## Model  8: mean_count_pot ~ s(dist, k = 5) + s(mws, k = 5) + s(sum_rain, 
##     k = 5)
## Model  9: mean_count_pot ~ s(dist, k = 5) + s(sum_rain, k = 5)
## Model 10: mean_count_pot ~ s(dist, k = 5) + s(sum_rain, k = 5) + mws
## Model 11: mean_count_pot ~ s(dist, k = 5) + s(mws, k = 5) + s(sum_rain, 
##     k = 5)
## Model 12: mean_count_pot ~ s(dist, k = 5, bs = "ts") + s(mws, k = 5, bs = "ts") + 
##     s(sum_rain, k = 5, bs = "ts")
## Model 13: mean_count_pot ~ s(dist, k = 5) + s(sum_rain, k = 5) + mws
##    Resid. Df Resid. Dev          Df Deviance          F    Pr(>F)    
## 1     329.00     248.10                                              
## 2     328.00     239.72  1.00019797     8.38    23.0239 2.443e-06 ***
## 3     328.00     236.49  0.00017108     3.22 51787.2571 2.104e-07 ***
## 4     327.00     230.81  1.00011438     5.69    15.6198 9.506e-05 ***
## 5     328.00     239.72 -1.00028547    -8.91    24.4745 1.209e-06 ***
## 6     324.01     204.37  3.99671315    35.35    24.3000 < 2.2e-16 ***
## 7     325.01     206.98 -1.00100428    -2.61     7.1723 0.0077645 ** 
## 8     324.02     204.41  0.98528685     2.57     7.1674 0.0080586 ** 
## 9     325.01     209.55 -0.99146246    -5.14    14.2473 0.0001994 ***
## 10    324.04     204.48  0.97643885     5.07    14.2777 0.0002125 ***
## 11    323.65     639.81  0.38652451  -435.32                         
## 12    324.67     667.59 -1.02220468   -27.78    74.6727 < 2.2e-16 ***
## 13    324.70     664.47 -0.02920554     3.12                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

0.3.5 Visualise the Models

0.3.6 Check Best Model Fit

0.3.6.1 Mod11.0 - s(Distance) + s(Windspeed) + s(Precipitation), family = tw()

## 
## Method: REML   Optimizer: outer newton
## full convergence after 9 iterations.
## Gradient range [-0.0002827365,-8.478081e-09]
## (score 310.1067 & scale 0.363966).
## Hessian positive definite, eigenvalue range [0.367564,2978.833].
## Model rank =  13 / 13 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##               k'  edf k-index p-value   
## s(dist)     4.00 3.50    0.86   0.010 **
## s(mws)      4.00 1.98    0.89   0.050 * 
## s(sum_rain) 4.00 2.83    0.91   0.065 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

0.4 Thoughts

This model, mod11.0, mean_pot_count ~ s(Distance) + s(Windspeed) + s(Precipitation) - family = tw(), lacks enough numbers of basis functions for two of three predictors, dist, wsp, but it’s close. Realistically we need to increase the k values for these predictors, but we’re lacking the data to do this.

Fit GAMs to dispersal patterns of Ascochyta conidia

A.H. Sparks

2020-02-25

0.1 Import Data

0.2 Fit GAMs

0.2.1 mod1 - s(Distance)

0.2.2 mod2 - s(Distance) + Precipitation

0.2.3 mod3 - s(Distance) + Windspeed

0.2.4 mod4 - s(Distance) + Windspeed + Precipitation

0.2.5 mod5 - s(Distance + Windspeed) + Precipitation

0.2.6 mod6 - s(Distance) + s(Windspeed) + Precipitation

0.2.7 mod7 - s(Distance) + s(Windspeed)

0.2.8 mod8 - s(Distance) + s(Windspeed) + s(Precipitation)

0.2.9 mod9 - s(Distance) + s(Precipitation)

0.2.10 mod10 - s(Distance) +s(Precipitation) + Windspeed

0.2.11 mod11.0 - s(Distance) + s(Windspeed) + s(Precipitation), family = tw()

0.2.12 mod11.` - s(Distance, bs = “ts”) + s(Windspeed, bs = “ts”) + s(Precipitation, bs = “ts”), family = tw()

0.2.13 mod12 - s(Distance) + s(Precipitation) + Windspeed, family = tw()

0.3 Compare the Models

0.3.1 AIC, BIC

0.3.2 R²

0.3.3 Coefficients

0.3.4 ANOVA

0.3.5 Visualise the Models

0.3.6 Check Best Model Fit

0.3.6.1 Mod11.0 - s(Distance) + s(Windspeed) + s(Precipitation), family = tw()

0.4 Thoughts

Fit GAMs to dispersal patterns of Ascochyta conidia

A.H. Sparks

2020-02-25

0.1 Import Data

0.2 Fit GAMs

0.2.1 mod1 - s(Distance)

0.2.2 mod2 - s(Distance) + Precipitation

0.2.3 mod3 - s(Distance) + Windspeed

0.2.4 mod4 - s(Distance) + Windspeed + Precipitation

0.2.5 mod5 - s(Distance + Windspeed) + Precipitation

0.2.6 mod6 - s(Distance) + s(Windspeed) + Precipitation

0.2.7 mod7 - s(Distance) + s(Windspeed)

0.2.8 mod8 - s(Distance) + s(Windspeed) + s(Precipitation)

0.2.9 mod9 - s(Distance) + s(Precipitation)

0.2.10 mod10 - s(Distance) +s(Precipitation) + Windspeed

0.2.11 mod11.0 - s(Distance) + s(Windspeed) + s(Precipitation), family = tw()

0.2.12 mod11.` - s(Distance, bs = “ts”) + s(Windspeed, bs = “ts”) + s(Precipitation, bs = “ts”), family = tw()

0.2.13 mod12 - s(Distance) + s(Precipitation) + Windspeed, family = tw()

0.3 Compare the Models

0.3.1 AIC, BIC

0.3.2 R2

0.3.3 Coefficients

0.3.4 ANOVA

0.3.5 Visualise the Models

0.3.6 Check Best Model Fit

0.3.6.1 Mod11.0 - s(Distance) + s(Windspeed) + s(Precipitation), family = tw()

0.4 Thoughts

0.3.2 R²